#5575 ⟨
a
,
b
,
c
|
ab
=
c
,
bbac
=
c
⟩
Up:
Monoid enumeration
Prev:
#5570
⟨
a
,
b
,
c
|
ab
=
c
,
bacc
=
c
⟩
Next:
#5578
⟨
a
,
b
,
c
|
ab
=
c
,
bbbc
=
c
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not right cancellative, because right multiplication by
d
is not injective:
b
2
db
⋅
d
=
d
and 1 ⋅
d
=
d
, however
b
2
db
≠ 1
Rewriting system
Format:
Pretty
Plain
Word:
Enter a word above to compute its normal form. Tips:
Lowercase letters stand for generators.
Spaces are ignored.
Numbers repeat the previous letter, e.g.
b90
.
Strategy:
Leftmost
Rightmost
Result:
1
1
Auxiliary generators:
d
=
ac
Reduction order:
Left-to-right recursive path with deg(
b
) = deg(
d
) = 0,
b
<
d
; deg(
c
) = deg(
a
) = 1,
c
<
a
Certificate
: derivations of all rewriting rules from the defining relations.
Morphocompletion
: how the auxiliary generators were found.
#
Rule
Proof
1.
b
(
bd
)
2
⇒
d
[5]
2.
c
⇒
b
2
d
[4]
3.
ab
⇒
b
2
d
[6]
4.
ad
⇒
dbd
[7]
# abc:ab=c,bbac=c bd/ca ac=d morph:2/1 bbdbd=d c=bbd ab=bbd ad=dbd